The reorientational behaviour of cyclohexane molecules in the rotator phase has been investigated with a Monte Carlo simulation in a cubic box with periodic boundary conditions. A previous simulation for state pints at normal pressure is extended to higher pressure. This enables us also to perform simulations along isochors and isotherms, thus to distinguish between isothermal density changes and isochoric temperature changes. Reorientational correlation functions for various molecular axes are calculated in order to analyse the orientational disorder. it was found that in the immediate neighbourhood to the low-temperature phase transition the orientational freedom is limited. At larger distances to the solid-solid transition line no preferred orientations can be detected. The reorientational behaviour changes significantly when a displacement of the molecular centers is allowed, in particular the otherwise retarded decay of the correlation function for the C3-axis is accelerated near the low-temperature phase boundary of solid I.